Synthesis of LPV Controllers With Low Implementation Complexity Based on a Reduced Parameter Set

A major difficulty encountered in the application of linear parameter-varying (LPV) control is the complexity of synthesis and implementation when the number of scheduling parameters is large. Often heuristic solutions involve neglecting individual scheduling parameters, such that standard LPV controller synthesis methods become applicable. However, stability and performance guarantees are rendered void, if controller designs based on an approximate model are implemented on the original plant. In this brief, a synthesis method for LPV controllers that achieves reduced implementation complexity is proposed. The method is comprised of first synthesizing an initial controller based on a reduced parameter set. Then closed-loop stability and performance guarantees are recovered with respect to the original plant, which is considered to be accurately modeled. Iteratively solving a nonconvex bilinear matrix inequality may further improve performance. A two-degrees-of-freedom (2-DOF) and three-degrees-of-freedom robotic manipulator is considered as an illustrative example, for which experimental results indicate a good performance for controllers of reduced scheduling order. Furthermore, in the 2-DOF case, controller performance has been significantly improved.